Hi,
I'm working on my dissertation in computer science and I'm desperately looking
for examples of the use of a particular form of equation. The equations I'm
looking for are recurrence's of the following form:
X(i1,...,in)=
f(X(i1+d11,...in+d1n),X(i1+d21,...,in+d2n),...,X(i1+dk1,...in+dkn))
Where:
X: is a state space indexed by integers i1,...,in. In computerese
this is an array of dimension n.
f: is the function I am looking for.
d11,...,dkn: is a set of fixed displacements from the destination X.
Ideally, I'd like the dimension (n) to be bigger than 2, the displacements
(d11,..dkn) to be small, preferably 0 or 1, and the number of
values of X (k) to also be small and fixed. However, I'd be interested in
seeing anything you think even approximates this.
In other words, what I'm looking for is examples of recurrences where the
destination value is a function of the values a small fixed distance away.
We call these near-neighbor reccurences.
Also, if your example equation has some important "real world" application,
that would be even better, but I'm looking for anything right now.
Any help (pointers, references, vague hints, etc.) will be appreciated.
Thanks,
- Bob Oehmke (oehmke at umich.edu)
p.s. Any examples I can use will score the owner an acknowledgement in my
thesis. I know its a small price, but I'm a poor grad. student,
recognition is all I have to give. :-)